THE RICE INSTITUTE
THE N^a.cON14- AND N^c^pJO17 REACTIONS FOR
BOMBARDING ENERGIES FROM 3 TO 5 MEV
by
EDWIN KASHY
A THESES
SUBMITTED TO THE FACULTY
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF ARTS
Houston, Texas
May, 1957
TABLE OF CONTENTS
I Introduction •••••••••••
II Experimental Procedure
III Experimental Results
1
••
2
........
8
IV Interpretation of the Angular Distribution
Data
V Conclusion
VI Acknowledgements
VII References
9
.
.
12
13
*
.
14
THE N14(a,a)N14 AND N14(a,p)o17 REACTIONS FOR
BOMBARDING ENERGIES FROM 3 TO 5 MEV
I.
INTRODUCTION:
The purpose of this work is the investigation of the scattering
and reaction resulting from the bombardment of H*4 with alpha particles
having energies from 3 to 5 Mev.
The N^4(a,p)Cp-7 reaction is of some
historical interest because it was the first of the laboratory induced
nuclear reactions.
by Rutherford.
The original experiments were performed in 1919
Subsequent work on this reaction has been done by R.
R. Roy} using Polonium alpha particles and nuclear plates, by N. P.
Heydenberg and G. M. Temmer^, using artificially accelerated alpha
particles with energies between 1.5 and 3*5 Mev, and others.
The reaction and scattering cross sections give information
about the positions and widths of energy levels of the compound nucleus
F-*-®
and an analysis of the data by the scattering matrix method as
S
described by J. M. Blatt and L. C. Biedenharn may lead to assignments
of total angular momentum and parity to the nuclear energy levels.
When N-^4 is bombarded with alpha particles, the following
reactions occur below 5 Mev:
N14
+
Re4 —*
N14
+ He4
017
+ #
-
1.198 Mev
(2)
1
-
2.073 Mev
(3)
017* + H
(l)
The first of these equations corresponds to elastic scattering
of alpha particles, the second to a reaction with the protons going
2
to the ground state of 6^, and the third to a reaction with the
protons going to the 0.875 Mev state of Cp^.
We have not so far been
able to observe this second proton group in our experiment;
the yield
of protons to the 0.875 Mev state is given by R. R. Roy,^ who used
photographic plates, to be 0.12 of the yield to the ground state of 0^7.
The analysis of the data is complicated by the large angular
momentum of the ground of 0^7,
( 1= 5/2+ ), because for a given value
of the spin and parity of a level in the compound nucleus F-^, there
are many allowed values of lp, the orbital angular momentum of the
outgoing proton.
II.
EXPERIMENTAL PROCEDURE?
The Rice Institute 5.5 Mev Van Der Graaff accelerator was used
to accelerate singly ionized alpha particles which were then deflected
through a 90° angle in a strong magnetic field.
The pa tides then
entered the large volume scattering chamber of the Rice Institute.
chamber is described in detail in the theses of C.
Henry,' and J. L. Russell, Jr. •
W. Riech,^
R.
The
R.
Briefly, it consists of a large
cylindrical chamber which is filled with gas at low pressure.
two detectors, each of which has a set of defining slits.
It has
The detectors
can be positioned from the outside of the chamber and the angles
measured on circular vernier scales.
counters using thin
(0.25)
The
detectors are scintillation
Thallium activated Cesium Iodide crystals
mounted on 6291 photomultiplier tubes.
The chamber is equipped with
two Butyl Pthalate manometers which give the pressures of the scattering
gas in the chamber and at the first stage in the differential pumping
3
tube of the chamber.
One side of each manometer is at high vacuum and
the other open to the chamber and the first stage in the differential
pumping tube respectively.
The difference of levels is read with a
cathetometer, and the accuracy of the readings is 0.456.
The difference
of levels, when multiplied by the density of the Butyl Pthalate, gives
the respective pressures.
Each set of slits defines an effective target thickness for the
incoming beam of alpha particles.
We can compute the target thickness
from measurements of slit dimensions and knowledge of the pressure and
of the temperature in the chamber.
For a pressure of 3.5 cm of oil
and at an alpha particle energy of 3 Mev, the target thickness at a
laboratory angle of 90° is 5.0 Kev.
Figure 1 shows a top view of the
scattering chamber and Figure 2 is a schematic of the slit system.
We can obtain the following expression for the differential
cross section in the laboratory system of coordinates,0
<L = tUjgfaLfl
dG
q Gn
where N = number of particles counted
e = charge of the alpha particle
n = number of target nuclei per unit volume
q = charge collected in the Faraday cup
0 = angle of scattering in the laboratory system of coordinates
G = geometric factor of the slit system, where G is given by
G =
and
A = area of the rear slit
E s
FIGURE 1
SCHEMATIC OF SLIT SYSTEM
(FIG.2)
4
w = width of the front slit
s = separation distance of the slits
R = distance from the rear slit to the axis of rotation of the
detector.
The quantities A and v were measured using a traveling micro¬
scope, while s and R were measured using a steel ruler.
The value
obtained for detector #1 for the December experiment was
lCT^ cm;
for the March experiment, Gq was 1.956 x 10*"^ cm;
= 1.396 x
for the
#2 detector Gj was 2.069 x 10”^ cm,
A check of the validity of the expression for the differential
scattering cross section was obtained from measurements of the scattering
of alpha particles by argon.
Figure 3 is a plot of the elastic scat¬
tering cross section of argon for the energy range of the nitrogen
experiments;
the experimental points, obtained from the data using the
G-factor, agree with the theoretical value at energies of 3.5 Mev and
higher.
The discrepancy at the lower energies is due to the state of
charge of the alpha particles which will be discussed later.
The transformation of the differential scattering cross section
from the laboratory system to the center of mass system of coordinates
is given by^
(Tern
* C(0)fflab
where
H.
1 + —4 Cos 0
for elastic scattering
BARNS /STERADIAN
(CM)
5
For a reaction,
C(G) = (1 - x2Sin2 0)^ [ x Cos 6 + (1 -
]”2
where
c2
-■
!L2a
1 +
£L
-1
s
^ M4
and
= mass of the incident particle
M2 = mass of the target nucleus
Mj = mass of the reaction particle observed at lab. angle 6
M4 = mass of the residual nucleus
E
= laboratory energy of the incident particle
Q
= energy release of the reaction.
The energy of the alphajaarticles as they enter the differential
pumping tube is obtained from knowledge of the magnetic field and of the
radius of the particle path in the 90° analyzing magnet of the Van Der
Graaff accelerator.
The magnetic field is determined by a lithium
moment magnetometer and the radius by the micrometer slit settings.
After entering the differential pumping tube and the chamber, the alpha
particles lose energy by collisions with "toe orbital electrons of the
gas.
The energy loss 3 s computed in the case of alpha particles on
argon from tabulated values of the stopping power,and for the case
of alpha particles on nitrogen, from the tabulated values of the
stopping power of air and Beths*s formula for the relative stopping
power.^
The following expression was obtained for the energy loss of
alpha particles of energy E in the path between the 90° magnet and the
gas target in the chamber:
6
AE a 1.225 X 1CT3 [ 17.9 p0 + 39.3 PX ] [(dE/dx)E ]
where AE is in Kev, P0 and Pi are the chamber and first stage pressures
in cm of oil respectively and dE/dx is expressed in Kev-cm^/mg.
In the
December experiment the pressure in the chamber was approximately 5 cm
of oil so that the energy loss was of 135 =* 14 Kev at 2.8 Mev and 87 + 9
Kev at 4.9 Mev.
In the January experiment, the pressure was reduced
to 3.8 cm of oil so that the maximum energy loss was of 85 + 9 Kev at
alpha energy of 3.8 Mev.
The accuracy of the above expression was
estimated to be of ten per cent.
to
.5%
This determined the energy at 2.8 Mev
and 4.9 Mev to ,2%,
The number of alpha particles incident upon the gas target was
determined by charge integration in the Faraday cup.
Before entering
the Faraday cup, the alpha particles go through an aluminum foil of
0.76 cm air equivalent thickness, which strips the orbital electrons
from the alpha particles and leaves most of the aloha particles doubly
ionized.
However, some of the alpha particles have a zero net charge
or are singly ionized.
The state of charge of the alpha particles
cannot be calculated but was determined by measuring the Rutherford
scattering of alpha particles on argon.
From the ratio of the expected
value of the Rutherford scattering to the experimental value obtained
assuming the state of charge of the alpha particles to be 2e, we can
obtain the average charge of the alpha as a function of the bombarding
energy.
The results are shown in Figure 4.
It can be seen that the
correction is negligible above 3.5 Mev but is of the order of ten per
cent at 2.7 Mev.
The scattering cross sections and reaction cross
7
sections obtained at alpha bombarding energy of less than
3*5
Mev were
corrected usinr the average charge per alpha particle as given in
Figure 4, because it is only at alpha energies below 3.5 Mev that the
charge of the alpha particles appeal^ to differ appreciably from the
value 2e.
We were able to observe both the scattering and reaction products
at the same time at the backward angle and on the same detector.
Figure 5 is a typical pulse height distribution on the 20-channel
analyser.
The energies of the alpha particles is of 1,2 Mev and that
of the protons of 0,8 Mev,
The alpha particles are well separated from
the protons, the protons in this particular instance belonging to the
groung state of 0^ group.
The separation of the alphas from the
protons in the same crystal, in this case Thallium activated Cesium
Iodide, comes from the fact that the alpha particles and the protons
exhaust the luminiseence centers along their path in the crystal? the
greater ran-e of the protons, although they have less energy than the
alpha oarticles, therefore results in a higher pulse.
Ibis explains
the separation of the proton group from the alpha group in Figure 5,
The charge integration was performed by discharging a capacitor
previously charred to a known potential.
The beam current from the
Faraday cup is used to discharge the capacitor down to zero voltage,
at which point a relay is made to close, terminating the measurement.
The capacitor used was calibrated by the A. C, bridge method against
a standard capacitor.
microfarads.
The value obtained for the capacity was 10.19
The capacitor was also calibrated in somewhat the same
manner as it was used for the charge integration.
Having determined
CHANNEL NUMBER
the time taken for the potential to decay from a value VQ to a value Vj
with a large resistance R connected across the capacitor, the capacity
was calculated from the relation:
t = RC Ln VQ/VX
The value of the capacity obtained in this way was 10,40 micro¬
farads, in good agreement with the bridge value,
III.
EXPERIMENTAL RESULTS?
Me have taken five excitation curves and two angular distributions
corresponding to energy levels in F-^.
through 12,
The results appear in Figures 6
The differential reaction cross section in the laboratory
system of coordinates is plotted for laboratory angle of 89°0' in
Figure 6 and for laboratory angle of 163°54‘, in Figure 7,
The
excitation curves for the case of elastic scattering are all given in
the center of mass system of coordinates.
Figures 8,9, and 10 represent
the elastic scattering cross section at center of mass angle of 54°44%
90°0’, and 168°24' respectively.
Figures 11 and 12 represent angular
distribution of the protons of the Cp-^ ground state group at alpha
particles bombarding energies of 3,11 and 3.72 Mev,
From the excitation curves, we are able to make a table of the
levels of the compound nucleus, F^a with the corresponding value of
the alpha particles bombarding energy and the width of the levels in
the lab in Kev(Table 1),
FIGURE 6
E(LAB), MEV
(LAB), MILLIBARNS/STER ADI AN.
ENERGY (LAB) IN MEV
Nl4(a,a)N14
-.24
0 ( CM) =
E(LAB), MEV
3.0
_L_
1
FIGURE 8
r
P
90
E (LAB), MEV
FIGURE 9
FIGURE 10
ANGULAR
DISTRIBUTION
E(LAB)=3.72 MEV
Mli
£(lab)Mey
Lavela Jin F18. M©v
3.09
6,82
95
3.72
7.30
68
4.00
7.52
45
4.05
7.56
80
4.11
7.61
50
4.28
7.74
150
4.50
7.91
38
4.55
7.95
90
.
1' (lab)Kex
9
Figure 13 represents the energy levels in
as given by Aj zenberg
and Lauritsen (1955),^ and the proposed scheme of levels, as given
in Table 1.
IV.
INTERPRETATION OF THE ANGULAR DISTRIBUTION DATA:13
If only a limited range of the orbital angular momentum lj of
the incident particle makes up a reaction, then the angular distribution
of the product particle contains no powers of Cos 0 greater than
(Coo 0)^-i.
The same limitation applies for the orbital angular
momentum of the product particles
if lp is the largest value of the
angular momentum of the product particle, then the highest power of
Cos 9 that makes up the distribution is 21p.
A similar limitation holds
relating to the spin of the level in the compound nucleus: if a
resonance corresponds to a level whose total angular momentum is J,
then the maximum power of Cos 0 in the angular distribution is 2J.
If the angular distribution is symetrical about 90°, then the wave
function represents a state of definite parity, either even or odd.
This in turn means either that a single state of the compound nucleus
is involved in the reaction or that interference, if any, involves
states of like parity.
At 3.72 Mev the proton angular distribution
can be fit by the combination of P0(Cos 9) + 1.2P2(Cos 0).
Since
this distribution is symetrical about 90°, it indicates a definite
parity of the wave function for the reaction, ie, there is little or
no interference from neighboring states of different parity.
Since the highest power of Cos 9 that appears in the 3.72 Mev
angular distribution is 2, the state is made up either of la = 1 or
ENERGY
LEVELS
IN
8.0
F18 MEV)
7.95
7.91
7.74
7.7
7.61
7.56
7.52
7.30
—.
7.1
6.85
6.82
1
a
c. Q
b.o
y
AJZENBERG8
PROPOSED
LAURITSEN(I955) LEVEL SCHEME
FIGURE 13
10
of lp = 1, or else it is a J = 1 state.
By considering the conservation
of angular momentum and of parity in the fA4(a,p)0l7'> where the 0^ is
left
in the ground state, we can tabulate the possible values of la
and lp that can make up the states in Fl® of given spin and parity.^
Table II
J of F18
Parity
0
even
not allowed
0
odd
1
3
1
even
0,2
2,4
1
odd
1
1,3
2
even
2
0,2,4
2
odd
1,3
1,3,5
3
even
2,4
0; 2,4,6
3
odd
3
1,3,5
l
_IP
The 3*72 Mev angular distribution of the protons rules out all
even parity states except for J = 1+.
The J = 0“ possibility is ruled
out because it would give an isotropic distribution.
The probability
of the state having a J^3 was thought small because of the large value
of the orbital angular momentum of the alpha particle required to make
up such a state.
Of the remaining possibilities, 3,e, J of 1+, 1”,
and 2“, the J = 1” state was investigated by computing a theoretical
angular distribution as outlined by Blatt and Biedenham^ for the
elastically scattered alpha particles.
Figure 14 is a plot of that
angular distribution with the data points obtained from the excitation
FIGURE
14
11
l,
curves at the various angles.
The results are inconclusive at this
point because the theoretical curve of Figure 14 assumes an isolated
resonance corresponding to an isolated level in the compound nucleus.
Other possibilities for the spin
been investigated.
The angular distribution for the 6,82 Mev level
is very nearly isotropic.
for that state.
and parity of the state have not yet
It is tempting to make the assignment J = 0“
However, in order to be able to make final assignments
of spin and parity to these and other states, more data must be taken
and all the possibilities investigated.
12
V.
CONCLUSION
In our investigation of the scattering and reaction resulting
from the bombardment of
with alpha particles, we were able to
assign previously unreported levels to F-^.
We have also restricted
the possible values of the spin and parity of the 7.30 Mev level and
our isotropic angular distribution of the 6.82 Mev level which agrees
with the work of Heydengerg and Temmer,2 has also restricted the possible
value of the parity for that state.
VI.
ACKNOWLEDGEMENTS
The author wishes to thank R. R. Henry, P. D. Miller, and
P. N. Dean for their help in operating the scattering chamber and in
obtaining the data.
He would like especially to thank P. D, Miller
for many helpful suggestions and discussions.
He would also like to
thank the staff of the Rice Institute Shop for their help in
maintaining the Scattering chamber.
To Dr. J. R. Risser go the author’s
very special thanks for his help and encouragement which have made
this work possible.
The author wishes to acknowledge the financial
assistance in the form of a fellowship received from the Rice Institute.
14
VII.
REFERENCES
1. R. R. Roy, Phys. Re/. 82, 227 (1951).
2. N. P. Heydenberg and G. M, Temmer, Phys. Rev. 2S» 89 (1953).
3. F. G. Champion and R. R. Roy, Proc. Roy. Soc.
(London) A 191.
269 (1947).
4. G, S. Mani, R. Pandhi, Proc. Indian Acad. Sci. ^OA, 61 (1954).
5. J. M. Blatt and L. C. Biedenharn, Revs. Modern Phys. 24. 258 (1952).
6. C. W. Reich, Phd Thesis, Rice Institute,
(1956).
7. R. R. Henry, M. A. Thesis, Rice Institute,
(1956),
8. J. L. Russel, Jr., M. A. Thesis, Rice Institute,
(1956),
9. J. B. Marion, Tables for the transformation of angular distribution
data from the laboratory system to the center of mass system,
The Rice Institute and Shell Development Company, Houston , Texas.
IP.
Ronald Fuchs and W.
'dialing, Stopping Cross Sections, Kellog
Radiation Laboratory, The California Institute of Technology,
Pasadena, California.
11. E. Segre, Editor, Experimental Nuclear Physics.
(John Wiley & Sons, Inc.,
Pol. 1, 200,
lev; York 1953).
12. F. Ajzenberg and T. Lauritsen, Revs, Modena Phys. 27, 77 (1955).
13. J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics.
(John Wiley & Sons, Inc., 1952).